Lovie Smith may want to be reunited with one of his former Chicago Bears quarterbacks in Tampa Bay.

Bears backup Josh McCown said Monday there are four teams that have contacted his representatives about signing with them as a free agent.

McCown would not reveal the teams, but ESPN Chicago reported that the Bucs, Jets, Texans and Bears are making a strong push to sign the 35-year-old veteran.

"I’m not going to get in to who I talked to,” McCown said during an appearance on ESPN's Mike and Mike show. “There is a window and there is legal tampering but there are some shades on that window so I don’t know out of respect to those teams if we want to get into that right now. We’ve talked to four teams. There have been good discussions. We’ll take those as they come and evaluate those situations.

"To leave Chicago, it will be a situation where I’m looking to compete to start or to start and be able to kind of grow more as a player. The only way as a player that you can do that is on the field. That will definitely be something that we are looking at. So we’ll see. We’ll see what opportunities come and where we are at tomorrow.”

McCown had a career year in 2013, going 3-2 with the Bears in relief of injured starter Jay Cutler, completing 149 of 224 pass attempts for 1,829 yards, 13 touchdowns and one interception. He finished the season as the NFL’s third highest-rated quarterback with a 109.0 passer rating

In Tampa Bay, McCown would be given every chance to compete with Mike Glennon for the starting job. The Jets also have a young quarterback in Geno Smith that struggled as a rookie. The Texans own the No. 1 overall pick in the draft.

Both Smith and general manager Jason Licht have said they weren't prepared to annoint Glennon as the Bucs' starting quarterback. After taking over for Josh Freeman, Glennon went 4-9 as a starter with 19 touchdowns and 9 interceptions. He completed 59.4 percent of his passes for 2.608 yards.

Teams can begin signing free agents at 4 p.m. Tuesday.

"Once it's open to signing, that's when things get more serious,'' McCown said. "Even now, there's still a lot more talk and feeling out.''

If the Bucs are able to sign McCown, it would not preclude them from drafting a quarterback. They currently have two on the roster -- Glennon and Mike Kafka. Smith has said he wants to bring four quarterbacks to training camp.

McCown's biggest selling point is his experience.

"The experience, having played in the NFL and started games and having played at a certain level over somebody who hasn't played yet,'' McCown said. "When you have a guy who has done it, there's a lot of value there.''

Signing McCown may lessen the urgency to play a rookie quarterback and give the Bucs some flexibility with the No. 7 overall pick.

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